A simple approach for charge renormalization of highly charged macro-ions

摘要

We revisit the popular notion of effective or renormalized charge, which is aconcept of central importance in the field of highly charged colloidal orpolyelectrolyte solutions. Working at the level of a linear Debye-H\"uckel liketheory only, we propose a simple, efficient and versatile method to predict thesaturated amount of charge renormalization, which is however a non-lineareffect arising at strong electrostatic coupling. The results are successfullytested against the numerical solutions of Poisson-Boltzmann theory for polyionsof various shapes (planar, cylindrical and spherical), both in the infinitedilution limit or in confined geometry, with or without added electrolyte. Ourapproach, accurate for monovalent micro-ions in solvents like water, is finallyconfronted against experimental results, namely the crystallization of chargedcolloidal suspensions and the osmotic coefficient of B-DNA solutions.